**C. Belingeri**

## A Recursion Formula for the Coefficients of Entire
Functions Satisfying an ODE

with Polynomial Coefficients

**Abstract:**

A recursion formula for the coefficients of entire functions which are solutions
of linear differential equations with polynomial coefficients is derived. Some
explicit examples are developed. The Newton sum rules for the powers of zeros of
a class of entire functions are constructed in terms of Bell polynomials.

**Keywords:**

Entire solutions of ODE with polynomial coefficients, recursion formulas for
coefficients, Newton sum rules for reciprocal of zeros, Bell polynomials.

**MSC 2000:** 65L99, 30D20, 30C10